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arXiv · 2502.04610

A note on logarithmic mean equicontinuity

Dominik Kwietniak·Jian Li·Habibeh Pourmand
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Abstract

We study the set of harmonic limits of empirical measures in topological dynamical systems. We obtain a characterization of unique ergodicity based of logarithmic (harmonic) mean convergence in place of Ces\`aro convergence. We introduce logarithmic mean equicontinuity and show that a topological dynamical system is logarithmically mean equicontinuous if and only if it is mean equicontinuous.

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Dominik Kwietniak, Jian Li, Habibeh Pourmand. 2025-02-07. A note on logarithmic mean equicontinuity. https://doi.org/10.1007/s10884-025-10457-z

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